DTL Basic Considerations Thanks to J Stovall for

DTL: Basic Considerations Thanks to J. Stovall, for the help! M. Comunian & F. Grespan

Out. Line • • • Design parameters Design Method Design of PMQ, Field Law, Lattice Beam dynamics optimization Example of a FODO and FFDD DTL Conclusion

DTL Parameters • • • • Particles is proton. Input energy of 3 Me. V. (β=0. 0798) Output energy of 50 Me. V. (β=0. 314) Frequency is 352. 2 MHz. Current of 70 m. A. Duty cycle 4%. Total peak power (SF*1. 2+Beam) < 6 MW. Total DTL length <20 m (inter tanks space? ). Input Transverse RMS emittance Norm. of 0. 22 mmmrad. (output of RFQ+10% in the MEBT) Input Longitudinal RMS emittance Norm. of 0. 32 mmmrad (output of RFQ). Input distribution Gaussian (5 sigma on size, i. e. a very large total emittance). Simulation Code: Trace. Win with a minimum of 10^5 particles (i. e. 1. 4 W for particle). Calculated matched input beam conditions. Constant PMQ gradient or Equipartitioning. PMQ size as Linac 4 PMQ tender.

Design method • • • Maximum of 1. 4 Ekp? -> limited By Moretti Criteria. Maximum of 2 MW power for Tanks. -> From Klystron limit. Maximum RF Tank length of 7 -8 m? -> From RF tuning. Maximum PMQ field of 50 -70 T/m? -> From manufacturing. Maximum output emittance? -> From SC Linac Acceptance. Maximum losses allowed? (1 W/m? ) -> From radioprotection. Maximize effective shunt impedance? -> From Cell design and Field stabilization. Equipartitioned BD design? -> SNS design rule. Field E 0 ramping? -> SNS yes, CERN no. Lattice? FFDD(CERN)? FODO? FFODDO(SNS)? O=space for steering/BPM. Intertank distance? 3β (CERN)? or 1 β (SNS)? Maximum Mechanical module length? ->2 m from manufacturing.

Moretti Criteria is more demanding respect to the Kilpatrick “Brave” factor • sparking in the region of collinear B & E fields. Clamp effects Sparking effects (@1. 7 kp) on Linac 4 DTL prototype

Flat or Ramped Field E 0? The idea is to model the longitudinal behavior of the field distribution with the goal of determining the dimensions of perturbations applied to the tank end walls that will pre-set the longitudinal field distribution to approximately that of the design. Shapes of the individual drift tubes are the same as the design except for the face angles. The ramped solution is better in term of performance.

DTL Example • FODO Lattice: – – Space inside DTL for steering and BPM. Optimizations of Shunt impedance by asymmetric cell. Reduce number of PMQ. High gradient of PMQ, from 54 T/m to 71 T/m. • FFDD Lattice: – No space inside DTL. – Low gradient of PMQ.

DTL Example SF runs from 3 to 50 Me. V Data collect and analysis on Excel Power by SF*1. 25 Design Summary Tank 1 2 3 Total No of Cells 66 29 24 119 Length m 7. 47 5. 75 5. 93 19. 15 Wfinal Mev 19. 20 34. 88 50. 26 Power MW 2. 050 2. 045 2. 072 6. 17

FODO const. G FODO Equip. G FFDD const. G FFDD Equip. G

Lattice FODO Const. G FODO Equip. G FFDD Const. G FFDD Equip. G # PMQ 62 62 119 G PMQ [T/m] 54 72 - 31 45. 5 51. 5 - 22. 5 Emit(x, y) increase [%] 16 14 13 15 Emit(z) increase [%] 26 14 23 13 Halo(x, y) increase [%] 59 32 48 30 Halo(z) increase [%] 14 34 41 35 The Equipartitioned design show less emittance and halo increase.

Longitudinal Acceptance of the DTL FODO const. G Emit [82%] = 8. 7326 Pi. deg. Me. V FODO Equip. G Emit [78%] = 11. 1151 Pi. deg. Me. V FFDD const. G Emit [84%] = 8. 7523 Pi. deg. Me. V FFDD Equip. G Emit [73%] = 12. 9853 Pi. deg. Me. V

Transverse Acceptance of the DTL FODO Const. G X-Xp Emit [82%] = 9. 2989 Pi. mm. mrad [ Norm. ] FODO Equip. G Y-Yp Emit [87%] = 10. 0178 Pi. mm. mrad [ Norm. ] FFDD Const. G X-Xp Emit [83%] = 12. 3347 Pi. mm. mrad [ Norm. ] FFDD Equip. G Y-Yp Emit [82%] = 9. 4390 Pi. mm. mrad [ Norm. ]

Errors study on the DTL example • Magnetic center respect the geometrical center shake of +/- 0. 2 mm • Yaw/pitch/Roll of +/-1°=17 mrad • Gradient error of +/-1% • All errors apply together with a Gaussian input beam distribution • 100 DTL generated. • 10^5 particles i. e. 1. 4 W for particles.

FODO const. G FODO Equip. G FFDD const. G FFDD Equip. G 10^5 particles; 10^2 DTL; Max Quad shake of X, Y ± 0. 2 mm; ± 1°; ± 1%

FODO const. G FODO Equip. G FFDD const. G FFDD Equip. G Quad shake of X, Y ± 0. 2 mm; ± 1°; ± 1%

FODO const. G max=65 W FODO Equip. G max=434 W FFDD const. G=130 W FFDD Equip. G max=1700 W Quad shake of X, Y ± 0. 2 mm; ± 1°; ± 1%

Steerers on FODO Lattice • Using the empty space it has been put steerers X; Y almost at 90° phase advance apart for tank and 2 BPMs. 8 Steerers for tank 1 4 steerers for tank 2 and 3

Max=5 W FODO const. G with 32 steerers

Max=14 W FODO Equip. G with 32 steerers

Conclusion on DTL example FFDD and FODO almost same PMQ grad. FFDD better output emittance. Constant Grad. more “robust” respects to errors. FODO more flexible and at lower cost. Steerers on FODO reduce the losses by 1 order of magnitude. • A possible solution with PMQ G=54 T/m -> as Linac 4 DTL tender. • Space for steerers and BPM -> low tolerance on PMQ and reduced intertank distance. • No problem by losses -> low tolerance on PMQ. • • •

Thank you!

Design Method • DTLFISH: design and optimization of the DTL shape from 3 to 50 Me. V. • Worksheet: import of DTLFISH data and fit cell by cell. • Worksheet : Synch. Phase, PMQ, Lattice and E 0, Es Fields design. • Worksheet : data for Trace. Win cell by cell, including TTF’ and TTF’’. • Trace. Win: Phase advance design and input matched conditions. • Trace. Win: Errors study.

Emittance evolution on the DTL UNIFORM Distribution GAUSSIAN Distribution The emittance increase depend from the input beam distribution

PMQ First DTL Cell CERN Linac 4 ID=22 mm L=45 mm Gmax=54 T/m • Difficult to housing the Quad on the first DTL cell. • The least expensive type has rectangular PM pieces. • The most performing is the Bullet shape. • Field clamp? • Bore aperture ID? • PMQ tolerance!!!

FODO FFDD FDO LATTICE DESIGN FFODDO FFDDO FD Particles density plot for different focusing scheme along the DTL

FODO const. G FODO Equip. G FFDD const. G FFDD Equip. G